Question 1208105
<pre>
Use capital letters B and G for boys and girls in the tennis club and
small letters b and g for boys and girls in the badminton club.  

The tennis club and badminton club have a total of 109 members.

B + G + b + g = 109

The number of boys in the tennis club is 6/11 the members of this club. 

B = (6/11)(B + G)

The number of girls in the badminton club is 4/9 the members of this club. 

g = (4/9)(b + g)

How many boys are there in both clubs.

Go to https://www.wolframalpha.com/

type in  B + G + b + g = 109,  B = (6/11)(B + G), g = (4/9)(b + g)

For "integer solution", read

b = 55n + 30, B = 30 - 54n, g = 44n + 24, G = 25 - 45n, n element Z

Then since they must all be non-negative, choose n = 0

b = 30, B = 30, g = 24, G = 25

Add the boys, B + b = 30 + 30 = 60

Edwin</pre>